If current is flowing in cardiac tissue, and if the myocardial fibres approach a sealed boundary at an angle, then the tissue within a few length constants of the boundary is polarised. This polarisation occurs when the cardiac tissue has different anisotropy ratios in the intracellular and extracellular spaces. This new mechanism of tissue polarisation is demonstrated using a simple, analytical model, and it is shown quantitatively that this polarisation can be nearly as large as that occurring near an electrode.